A method for constructing a curved surface solar concentrator with uniform light absorption on the surface of the absorber

Abstract

This invention relates to a method for constructing a curved solar concentrator with uniform light reception on the absorber surface, belonging to the field of solar photovoltaic and photothermal technology. This invention utilizes differential geometry theory to construct a system of first-order nonlinear differential equations relating the concentrator's reflective surface (x and y coordinates) to the radius r of the circular absorber. The reflective surface profile parameters are obtained through iterative solutions. A discrete point lattice is obtained, with the spatial straight-line distance and maximum deviation between adjacent iteration coordinate points not exceeding 2 mm as the convergence criterion. A curved concentrator model is then generated through spline curve fitting. The energy flux density distribution on the absorber surface is obtained using the ray tracing software Tracepro, and the uniformity of the energy flux distribution is verified using a relative deviation not exceeding ±10% of the average value. This invention achieves uniform distribution of incident solar radiation on the absorber surface, eliminates local hot spots, significantly reduces thermal stress gradients, and improves the photothermal conversion efficiency and operational stability of the solar concentrator system.

Description

Technical Field

[0001] This invention relates to a method for constructing a curved solar concentrator with uniform light absorption on the surface of the absorber, belonging to the field of solar photothermal conversion and concentrating utilization technology. Background Technology

[0002] The inherently low energy flux density of solar radiation limits its direct application in medium- and high-temperature thermal utilization. Employing geometric concentrating technology is an effective way to increase the energy flux density of solar radiation.

[0003] During operation, conventional solar concentrators often exhibit a significantly non-uniform distribution of concentrated solar radiation on the absorber surface. This non-uniform radiation field directly leads to a non-linear temperature gradient distribution on the absorber surface, with localized areas even exhibiting temperature field differences of orders of magnitude. This severely restricts the photothermal conversion efficiency, operational stability, and lifespan of the solar thermal collection system. Particularly for circular absorbers (such as solar vacuum tubes), the thermal stress concentration caused by non-uniform light exposure can lead to absorber cracking and failure, becoming a bottleneck problem restricting the development of solar concentrating technology.

[0004] To improve the uniformity of energy flux distribution on the absorber surface, existing research mainly employs methods such as surface optimization design, freeform surface light modulation, and the introduction of secondary optical elements to enhance light concentration uniformity. However, these methods often lead to complex geometric structures of the concentrator surface or significantly increase system optical losses and manufacturing costs. Furthermore, a mature theoretical framework for the uniform light concentration mechanism of circular absorbers has not yet been established. Therefore, it is urgent to theoretically construct a uniformly receiving solar concentrator model suitable for circular absorbers and reveal the intrinsic optical mechanism in its light concentration process. Summary of the Invention

[0005] To address the technical problems of existing conventional concentrators, such as uneven energy flow distribution on the surface of curved absorbers, large heat flow gradients, and susceptibility to cracking and damage, this invention provides a method for constructing a curved solar concentrator with uniform light reception on the absorber surface. By establishing a mathematical mapping relationship between the light vector and the concentrating surface shape, the uniform distribution of incident solar radiation on the surface of the circular absorber is achieved, thereby improving the photothermal conversion efficiency and operational stability of the solar concentrating system.

[0006] A method for constructing a curved solar concentrator with uniform light reception on the surface of the absorber, the curved solar concentrator comprising a curved concentrating surface 1 and a cylindrical absorber 2, the cylindrical absorber 2 being disposed on the inner side of the curved surface of the curved concentrating surface 1, the curved concentrating surface 1 being used to uniformly reflect sunlight incident perpendicularly to the curved concentrating surface 1 onto the light-receiving surface of the cylindrical absorber 2, forming a uniform energy flux density distribution; under ideal optical conditions, i.e., when the optical loss of the curved concentrating surface to the incident light is ignored, parallel incident light rays irradiate the curved concentrating surface perpendicularly or approximately perpendicularly, and after reflection, are projected onto the outer surface of the cylindrical absorber in a uniformly distributed manner, thereby forming a uniform energy flux density distribution on the surface of the cylindrical absorber. The specific steps are as follows: S1. Obtain initial design parameters. Establish a Cartesian coordinate system with the center of the absorber as the origin O. The radius of the cylindrical absorber is r, the geometric concentration ratio of the curved solar concentrator is C, the central angle corresponding to the incident ray incident on the cylindrical absorber is β, and the incident parallel ray enters the concentrator opening along the negative y-axis. S2. Based on the initial design parameters, construct a mathematical model of the geometric relationship of the reflector surface of the curved solar concentrator and generate a three-dimensional curved surface. Establish a first-order nonlinear differential equation between the abscissa x and ordinate y of the reflector surface of the concentrator and the radius r of the cylindrical absorber. S3. When the central angle β corresponding to the incident light ray incident on the cylindrical absorber is greater than zero, β is iteratively calculated with a step size h. The convergence criterion is set as the iteration error d not exceeding 2mm and the maximum deviation e. max The iteration error d is no greater than 2mm, and the iteration error is the coordinate point (x) obtained from two adjacent iterations. i y i ), (x i+1 y i+1 The straight-line distance between them; Based on the current point coordinates and the derivative of the first-order nonlinear differential equation at that point, the next iteration point is predicted using the linear equation, and iterative calculation is performed until convergence. If the iteration error is greater than 2mm, the feedback optimization mechanism is activated, the central angle β is finely adjusted by ±1°, and iterative calculation is performed again until convergence, so as to obtain the discrete point lattice of surface geometric coordinates at each position of the curved light-collecting surface. S4. The discrete point lattice of the surface geometric coordinates is fitted with a spline curve, using natural boundary conditions, and the second derivatives of the first and last endpoints are set to zero, i.e., M0=0 and M n =0, and the second derivatives M1 to M of each internal node are obtained by the chasing method. n-1 In each interval [x i x i+1 On the [x], a curved focusing surface is constructed using the formula in the interval [x] i x i+1The surface equation of ] is used to generate a curved surface condenser model in 3D modeling software based on the surface equation of each interval; S5. Using the ray tracing software Tracepro, simulate the energy flux density distribution in different regions of the cylindrical absorber surface under the condition of perpendicular sunlight incident at an incident angle of 0°. By analyzing the energy flux density distribution map, verify the uniformity of the energy flux density distribution.

[0007] Preferably, the differential equations between the abscissa x and ordinate y of the concentrator reflector surface and the radius r of the cylindrical absorber in step S2 are as follows: ; The formula for calculating β is: ; In the formula, x is the abscissa of the curved solar concentrator, y is the ordinate of the curved solar concentrator, r is the radius of the cylindrical absorber, and β is the central angle corresponding to the incident light rays incident on the cylindrical absorber.

[0008] More preferably, the formula for calculating the iteration error d in step S3 is: ; The iterative calculation method for the central angle β corresponding to the incident light ray incident on the cylindrical absorber is as follows: β0 is 0, β n It is 0.5π. The , ; In the formula, β i For the i-th discrete point (x) i ,y i At point ), the central angle corresponding to the incident ray incident on the cylindrical absorber, β i-1 For the (i-1)th discrete point (x) i-1 ,y i-1 At point ( ), the central angle corresponding to the incident ray incident on the cylindrical absorber, r is the radius of the cylindrical absorber, h is the step size of the iterative calculation, and C con,i The geometric concentration ratio contributed by the reflective surface of the curved solar concentrator in the i-th iteration.

[0009] Preferably, in step S4, the interval [x] i x i+1 The equation formula for the surface shape of ] is: S i (x)=a i +b i (xx i )+c i (xx i ) 2+d i (xx i ) 3 ; In the formula, S i (x) is the surface shape function of the i-th interval, a i Let y be the ordinate of the left endpoint of the i-th interval. i b i The coefficient of the linear term in the polynomial represents the curve at x. i The slope at c i For M i / 2,d i The coefficients of the cubic term in the polynomial represent the interval [x]. i x i+1 The rate of change of the inner second derivative, b i The formula for calculation is: ; d i The formula for calculation is: ; In the formula, M i+1 For the interval [x i x i+1 Internal node x i+1 The second derivative, M i For the interval [x i x i+1 Internal node x i The second derivative of , where h is the step size.

[0010] Preferably, the method for verifying the uniformity of energy flux density distribution in step S5 is as follows: In step S5, the curved surface concentrator model constructed according to the mathematical model is simulated in Tracepro under the condition of 0° incident angle to obtain the energy flux density distribution on the surface of the cylindrical absorber; the average value of the energy flux density is calculated and compared with the energy flux density at each point; if the deviation of the energy flux density of the entire light-receiving area from the average value does not exceed ±10%, the energy flux density distribution is considered to be uniform; otherwise, the central angle β corresponding to the incident light rays incident on the cylindrical absorber is adjusted and redesigned until the condition for uniform energy flux density distribution is met.

[0011] The beneficial effects of this invention are: (1) The present invention has uniform energy flow distribution: the reflective surface is precisely constructed by differential geometry theory to achieve uniform energy flow distribution on the surface of the absorber, eliminate local hot spots and significantly reduce thermal stress gradient; (2) The optical configuration of the present invention is accurate: the proposed differential mapping model can customize the reflective surface shape according to different light concentration ratio requirements, providing a high-precision geometric construction tool for non-imaging optical systems; (3) Improved photothermal properties of the present invention: uniform light exposure suppresses nonlinear fluctuations in the temperature field, improves the temperature rise characteristics of the heat transfer medium, and enhances the photothermal conversion efficiency and heat output stability of the system. (4) The structure of the present invention is easy to integrate: under the premise of ensuring uniformity, the cross-sectional profile of the concentrator is optimized, which makes it easy to modularly integrate with the existing vacuum heat collection tube array, significantly reducing the manufacturing difficulty of the system. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of a curved solar concentrator structure. Figure 2 A schematic diagram of the initial design parameters for a curved solar concentrator; Figure 3 A schematic diagram of the model simulation verification using Tracepro software when r=1 and C=3 (incident angle 0°). Figure 4 A schematic diagram of the model simulation verification using Tracepro software when r=1.5 and C=1.5 (incident angle 0°). Figure 5 A schematic diagram of the model simulation verification using Tracepro software when r=2 and C=4 (incident angle 0°). Detailed Implementation

[0013] The present invention will be further described in detail below with reference to specific embodiments, but the scope of protection of the present invention is not limited to the content described.

[0014] This invention discloses a method for constructing a curved solar concentrator with uniform light reception on the absorber surface. The curved solar concentrator includes a curved concentrating surface 1 and a cylindrical absorber 2. The cylindrical absorber 2 is disposed on the inner side of the curved surface of the concentrating surface 1. The curved concentrating surface 1 is used to uniformly reflect sunlight incident perpendicularly to the concentrating surface 1 onto the light-receiving surface of the cylindrical absorber 2, forming a uniform energy flux density distribution. Under ideal optical conditions, i.e., when the optical loss of the concentrating surface to the incident light is ignored, parallel incident light rays irradiate the concentrating surface perpendicularly or approximately perpendicularly. After reflection, they are projected onto the outer surface of the cylindrical absorber in a uniformly distributed manner, thereby forming a uniform energy flux density distribution on the surface of the cylindrical absorber (see...). Figure 1 ).

[0015] Example 1: This example uses a circular absorber with radius r=1 and a geometric concentration ratio C=3 for the uniform concentrator. A method for constructing a curved solar concentrator with uniform light reception on the absorber surface is described (see...). Figure 2 and 3 The specific steps are as follows: S1. Obtain initial design parameters. Establish a Cartesian coordinate system with the center of the absorber as the origin O. The radius of the cylindrical absorber is r=1, the geometric concentration ratio of the curved solar concentrator is C=3, the central angle corresponding to the incident ray incident on the cylindrical absorber is β, and the incident parallel ray enters the concentrator opening along the negative y-axis. The external environmental irradiance is 1000 W / m². 2 ; S2. Based on the initial design parameters, a mathematical model of the geometric relationship of the curved solar concentrator reflector surface is constructed and a three-dimensional curved surface is generated. The differential equations between the abscissa x and ordinate y of the concentrator reflector surface and the radius r of the cylindrical absorber are established. The differential equations between the abscissa x and ordinate y of the concentrator reflector surface and the radius r of the cylindrical absorber are as follows: ; The formula for calculating β is: ; In the formula, x is the abscissa of the curved solar concentrator, y is the ordinate of the curved solar concentrator, r is the radius of the cylindrical absorber, and β is the central angle corresponding to the incident light rays incident on the cylindrical absorber. S3. When the central angle β corresponding to the incident light ray incident on the cylindrical absorber is greater than zero, β is iteratively calculated with a step size h = 0.66. The convergence criterion is set as the iteration error d not exceeding 2 mm and the maximum deviation e max The iteration error d is no greater than 2mm, and the iteration error is the coordinate point (x) obtained from two adjacent iterations. i y i ), (x i+1 y i+1 The linear distance between the two points; the formula for calculating the iteration error d is: ; The iterative calculation method for the central angle β corresponding to the incident light ray incident on the cylindrical absorber is as follows: β0 is 0, β n It is 0.5π. The , ; In the formula, β i For the i-th discrete point (x) i ,y i At point ), the central angle corresponding to the incident ray incident on the cylindrical absorber, β i-1 For the (i-1)th discrete point (x) i-1 ,y i-1 At point ( ), the central angle corresponding to the incident ray incident on the cylindrical absorber, r is the radius of the cylindrical absorber, h is the step size of the iterative calculation, and C con,iThe geometric concentration ratio contributed by the i-th reflecting surface of the curved solar concentrator; Based on the current point coordinates and the derivative of the differential equation at that point, the next iteration point is predicted using a linear equation, and iterative calculations are performed until convergence. If the iteration error is greater than 2mm, a feedback optimization mechanism is activated, the central angle β is finely adjusted by ±1°, and iterative calculations are performed again until convergence, resulting in a discrete lattice of surface geometric coordinates at each position of the curved light-gathering surface. In this embodiment, 9 equally spaced discrete coordinate points (x...) are calculated. i y i The values ​​are (1.00, -2.5), (1.66, -2.261787), (2.32, -1.94838), (2.98, -1.56417), (3.64, -1.115011), (4.30, -0.606459), (4.96, -0.045184), (5.62, 0.560858), and (6.28, 1.213968), respectively. The curved light-gathering surface is divided into 8 intervals with a step size h = 0.66. In this embodiment, the iteration error d is 0.81 mm, and the maximum deviation e is... max The value is 0.93 mm, satisfying the iteration error d ≤ 2 mm and e max If the deviation is ≤2mm, and this level is within the allowable range of a precision optical system, then the geometric model is reliable; S4. The discrete point lattice of the surface geometric coordinates is fitted with a natural cubic spline curve. Natural boundary conditions are used, and the second derivatives at the first and last endpoints are set to zero, i.e., M0=0 and M8=0. The second derivatives M1 to M7 of each internal node are obtained by the chasing method as 0.22125, 0.1506, 0.1524, 0.1351, 0.1258, 0.0877, and 0.1404, respectively. In each interval [x...] i x i+1 On the [x], a curved focusing surface is constructed using the formula in the interval [x] i x i+1 The surface equation of ] is used to generate a curved surface condenser model in 3D modeling software based on the surface equation of each interval; the interval [x] i x i+1 The equation formula for the surface shape of ] is: S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 ; In the formula, S i(x) is the surface shape function of the i-th interval, a i Let y be the ordinate of the left endpoint of the i-th interval. i b i The coefficient of the linear term in the polynomial represents the curve at x. i The slope at c i For M i / 2,d i The coefficients of the cubic term in the polynomial represent the interval [x]. i x i+1 The rate of change of the inner second derivative, b i The formula for calculation is: ; d i The formula for calculation is: ; In the formula, M i+1 For the interval [x i x i+1 Internal node x i+1 The second derivative, M i For the interval [x i x i+1 Internal node x i The second derivative, where h is the step size; The eight-segment piecewise fitting curve equations of the concentrator surface shape were calculated and obtained as follows: (1) In the interval [1.00, 1.66], S0(x)=-2.5+0.3366(x-1)+0.05585(x-1) 3 ; (2) In the interval [1.66, 2.32], S1(x)=-2.261787+0.4096(x-1.66)+0.110625(x-1.66) 2 -0.01784(x-1.66) 3 ; (3) In the interval [2.32, 2.98], S2(x)=-1.94838+0.5322(x-2.32)+0.0753(x-2.32) 2 +0.0004545(x-2.32) 3 ; (4) In the interval [2.98, 3.64], S3(x)=-1.56417+0.6321(x-2.98)+0.0762(x-2.98) 2 -0.00437(x-2.98) 3; (5) In the interval [3.64, 4.30], S4(x)=-1.115011+0.7269(x-3.64)+0.06755(x-3.64) 2 -0.00235(x-3.64) 3 ; (6) In the interval [4.30, 4.96], S5(x)=-0.606459+0.8131(x-4.30)+0.0629(x-4.30) 2 -0.00962(x-4.30) 3 ; (7) In the interval [4.96, 5.62], S6(x)=-0.045184+0.8835(x-4.96)+0.04385(x-4.96) 2 +0.01331(x-4.96) 3 ; (8) In the interval [5.62, 6.28], S7(x)=0.560858+0.9587(x-5.62)+0.0702(x-5.62) 2 -0.03545(x-5.62) 3 ; The first and second derivatives of the curved focusing surface are continuous at the connection points by using a cubic spline interpolation algorithm to eliminate false hot spots in optical simulation. S5. Using the ray tracing software Tracepro, the energy flux density distribution in different regions of the cylindrical absorber surface was simulated under the condition of perpendicular sunlight incidence (0° incident angle). The uniformity of the energy flux density distribution was verified by analyzing the energy flux density distribution map. Specifically, the curved surface concentrator model constructed according to the mathematical model was simulated in Tracepro under the condition of 0° incident angle to obtain the energy flux density distribution on the surface of the cylindrical absorber. The distribution of reflected light on the curved surface of the cylindrical absorber with radius r=1 was tracked and captured, and the total absorbed luminous flux of the system was found to be 762.38W, with the average energy flux density calculated to be 1.27kW / m². 2 The energy flux density is compared with the energy flux density at each point. If the deviation of the energy flux density of the entire light-receiving area from the average value does not exceed ±10%, the energy flux density distribution is considered to be uniform. Otherwise, the central angle β corresponding to the incident light rays incident on the cylindrical absorber is adjusted and redesigned until the condition for uniform energy flux density distribution is met. In this embodiment, the energy flux density of all light-receiving areas deviates from the average value by 7.8%, which is less than the preset threshold of 10%. Therefore, the energy flux density distribution on the cylindrical absorption surface in this embodiment is uniform.

[0016] Example 2: This example uses a circular absorber radius r=1.5 and sets the geometric concentration ratio C=1.5 for the uniform concentrator. A method for constructing a curved solar concentrator with uniform light reception on the absorber surface is described (see...). Figure 2 and 4 The specific steps are as follows: S1. Obtain initial design parameters. Establish a Cartesian coordinate system with the center of the absorber as the origin O. The radius of the cylindrical absorber is r=1.5, the geometric concentration ratio of the curved solar concentrator is C=1.5, the central angle corresponding to the incident ray incident on the cylindrical absorber is β, and the incident parallel ray enters the concentrator opening along the negative y-axis. The external environmental irradiance is 1000W / m². 2 ; S2. Based on the initial design parameters, a mathematical model of the geometric relationship of the curved solar concentrator reflector surface is constructed and a three-dimensional curved surface is generated. The differential equations between the abscissa x and ordinate y of the concentrator reflector surface and the radius r of the cylindrical absorber are established. The differential equations between the abscissa x and ordinate y of the concentrator reflector surface and the radius r of the cylindrical absorber are as follows: ; The formula for calculating β is: ; In the formula, x is the abscissa of the curved solar concentrator, y is the ordinate of the curved solar concentrator, r is the radius of the cylindrical absorber, and β is the central angle corresponding to the incident light rays incident on the cylindrical absorber. S3. When the central angle β corresponding to the incident light ray incident on the cylindrical absorber is greater than zero, β is iteratively calculated with a step size h = 0.8. The convergence criterion is set as the iteration error d not exceeding 2 mm and the maximum deviation e max The iteration error d is no greater than 2mm, and the iteration error is the coordinate point (x) obtained from two adjacent iterations. i y i ), (x i+1 y i+1 The linear distance between the two points; the formula for calculating the iteration error d is: ; The iterative calculation method for the central angle β corresponding to the incident light ray incident on the cylindrical absorber is as follows: β0 is 0, β n It is 0.5π. The , ; In the formula, β i For the i-th discrete point (x) i ,y i At point ), the central angle corresponding to the incident ray incident on the cylindrical absorber, β i-1 For the (i-1)th discrete point (x) i-1 ,y i-1 At point ( ), the central angle corresponding to the incident ray incident on the cylindrical absorber, r is the radius of the cylindrical absorber, h is the step size of the iterative calculation, and C con,i The geometric concentration ratio contributed by the i-th reflecting surface of the curved solar concentrator; Based on the current point coordinates and the derivative of the differential equation at that point, the next iteration point is predicted using a linear equation, and iterative calculations are performed until convergence. If the iteration error is greater than 2mm, a feedback optimization mechanism is activated, the central angle β is finely adjusted by ±1°, and iterative calculations are performed again until convergence, resulting in a discrete lattice of surface geometric coordinates at each position of the curved light-gathering surface. In this embodiment, 9 equally spaced discrete coordinate points (x...) are calculated. i y i The values ​​are (1.500000, -1.875000), (2.300000, -1.642310), (3.100000, -1.273489), (3.900000, -0.763741), (4.700000, -0.109705), (5.500000, 0.690127), (6.300000, 1.639641), (7.100000, 2.743126), and (7.900000, 4.004758), respectively. The curved light-gathering surface is divided into 8 intervals with a step size h = 0.8. In this embodiment, the iteration error d is 1.12 mm, and the maximum deviation e is... max The value is 1.49 mm, satisfying the iteration error d ≤ 2 mm and e max If the deviation is ≤2mm, and this level is within the allowable range of a precision optical system, then the geometric model is reliable; S4. The discrete point lattice of the surface geometric coordinates is fitted with a natural cubic spline curve. Natural boundary conditions are used, and the second derivatives at the first and last endpoints are set to zero, i.e., M0=0 and M8=0. The second derivatives M1 to M7 of each internal node are obtained by the chasing method as 0.4682, 0.4421, 0.4015, 0.3566, 0.3021, 0.2355, and 0.1428, respectively. In each interval [x...] i x i+1 On the [x], a curved focusing surface is constructed using the formula in the interval [x] i x i+1 The surface equation of ] is used to generate a curved surface condenser model in 3D modeling software based on the surface equation of each interval; the interval [x]i x i+1 The equation formula for the surface shape of ] is: S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 ; In the formula, S i (x) is the surface shape function of the i-th interval, a i Let y be the ordinate of the left endpoint of the i-th interval. i b i The coefficient of the linear term in the polynomial represents the curve at x. i The slope at c i For M i / 2,d i The coefficients of the cubic term in the polynomial represent the interval [x]. i x i+1 The rate of change of the inner second derivative, b i The formula for calculation is: ; d i The formula for calculation is: ; In the formula, M i+1 For the interval [x i x i+1 Internal node x i+1 The second derivative, M i For the interval [x i x i+1 Internal node x i The second derivative, where h is the step size; The eight-segment piecewise fitting curve equations of the concentrator surface shape were calculated and obtained as follows: (1) In the interval [1.5, 2.3], S0(x)=-1.875000+0.166312(x-1.5)+0.000000(x-1.5) 2 +0.097542(x-1.5) 3 ; (2) In the interval [2.3, 3.1], S1(x)=-1.642310+0.540875(x-2.3)+0.234100(x-2.3) 2 -0.005437(x-2.3)3 ; (3) In the interval [3.1, 3.9], S2(x)=-1.273489+0.871215(x-3.1)+0.221050(x-3.1) 2 -0.008458(x-3.1) 3 ; (4) In the interval [3.9, 4.7], S3(x)=-0.763741+1.157842(x-3.9)+0.200750(x-3.9) 2 -0.009333(x-3.9) 3 ; (5) In the interval [4.7, 5.5], S4(x)=-0.109705+1.455612(x-4.7)+0.178300(x-4.7) 2 -0.011312(x-4.7) 3 ; (6) In the interval [5.5, 6.3], S5(x)=0.690127+1.711235(x-5.5)+0.151050(x-5.5) 2 -0.013875(x-5.5) 3 ; (7) In the interval [6.3, 7.1], S6(x)=1.639641+1.968742(x-6.3)+0.117750(x-6.3) 2 -0.019312(x-6.3) 3 ; (8) In the interval [7.1, 7.9], S7(x)=2.743126+2.215547(x-7.1)+0.071400(x-7.1) 2 -0.029750(x-7.1) 3 ; The first and second derivatives of the curved focusing surface are continuous at the connection points by using a cubic spline interpolation algorithm to eliminate false hot spots in optical simulation. S5. Using the ray tracing software Tracepro, the energy flux density distribution in different regions of the cylindrical absorber surface was simulated under the condition of perpendicular sunlight incidence (0° incident angle). The uniformity of the energy flux density distribution was verified by analyzing the energy flux density distribution map. Specifically, the curved surface concentrator model constructed according to the mathematical model was simulated in Tracepro under the condition of 0° incident angle to obtain the energy flux density distribution on the surface of the cylindrical absorber. The distribution of reflected light on the curved surface of the cylindrical absorber with radius r=1.5 was tracked and captured, and the total absorbed luminous flux of the system was found to be 894.7W, with the average energy flux density calculated to be 1.5kW / m². 2 The energy flux density is compared with the energy flux density at each point. If the deviation of the energy flux density of the entire light-receiving area from the average value does not exceed ±10%, the energy flux density distribution is considered to be uniform. Otherwise, the central angle β corresponding to the incident light rays incident on the cylindrical absorber is adjusted and redesigned until the condition for uniform energy flux density distribution is met. In this embodiment, the energy flux density of all light-receiving areas deviates from the average value by 8.3%, which is less than the preset threshold of 10%. Therefore, the energy flux density distribution on the cylindrical absorption surface in this embodiment is uniform.

[0017] Example 3: In this example, with a circular absorber radius r=2 and a geometric concentration ratio C=4 for the uniform concentrator, a method for constructing a curved solar concentrator with uniform light reception on the absorber surface is described (see...). Figure 2 and 5 The specific steps are as follows: S1. Obtain initial design parameters. Establish a Cartesian coordinate system with the center of the absorber as the origin O. The radius of the cylindrical absorber is r=2, the geometric concentration ratio of the curved solar concentrator is C=4, the central angle corresponding to the incident ray incident on the cylindrical absorber is β, and the incident parallel ray enters the concentrator opening along the negative y-axis. The external environmental irradiance is 1000W / m². 2 ; S2. Based on the initial design parameters, a mathematical model of the geometric relationship of the curved solar concentrator reflector surface is constructed and a three-dimensional curved surface is generated. The differential equations between the abscissa x and ordinate y of the concentrator reflector surface and the radius r of the cylindrical absorber are established. The differential equations between the abscissa x and ordinate y of the concentrator reflector surface and the radius r of the cylindrical absorber are as follows: ; The formula for calculating β is: ; In the formula, x is the abscissa of the curved solar concentrator, y is the ordinate of the curved solar concentrator, r is the radius of the cylindrical absorber, and β is the central angle corresponding to the incident light rays incident on the cylindrical absorber. S3. When the central angle β corresponding to the incident light ray incident on the cylindrical absorber is greater than zero, β is iteratively calculated with a step size h = 0.5. The convergence criterion is set as the iteration error d not exceeding 2 mm and the maximum deviation e max The iteration error d is no greater than 2mm, and the iteration error is the coordinate point (x) obtained from two adjacent iterations. i y i ), (x i+1 y i+1 The linear distance between the two points; the formula for calculating the iteration error d is: ; The iterative calculation method for the central angle β corresponding to the incident light ray incident on the cylindrical absorber is as follows: β0 is 0, β n It is 0.5π. The , ; In the formula, β i For the i-th discrete point (x) i ,y i At point ), the central angle corresponding to the incident ray incident on the cylindrical absorber, β i-1 For the (i-1)th discrete point (x) i-1 ,y i-1 At point ( ), the central angle corresponding to the incident ray incident on the cylindrical absorber, r is the radius of the cylindrical absorber, h is the step size of the iterative calculation, and C con,i The geometric concentration ratio contributed by the i-th reflecting surface of the curved solar concentrator; Based on the current point coordinates and the derivative of the differential equation at that point, the next iteration point is predicted using a linear equation, and iterative calculations are performed until convergence. If the iteration error is greater than 2mm, a feedback optimization mechanism is activated, the central angle β is finely adjusted by ±1°, and iterative calculations are performed again until convergence, resulting in a discrete lattice of surface geometric coordinates at each position of the curved light-gathering surface. In this embodiment, 47 equally spaced discrete coordinate points (x...) are calculated. i y iThe values ​​are (2, -5), (2.5, -4.83353), (3, -4.63652), (3.5, -4.408408), (4, -4.148634), (4.5, -3.85667), (5, -3.531995), (5.5, -3.174151), (6, -2.782713), (6.5, -2.357307), (7, -1.897622), (7.5, -1.403408), and (8, -0.8744). 79), (8.5, -0.310717), (9, 0.28793), (9.5, 0.92145), (10, 1.589767), (10.5, 2.292747), (11, 3.030197), (11.5, 3.801876), (12, 4.607494), (12.5, 5.446722), (13, 6.319192), (13.5, 7.224505), (14, 8.162239), (14). 5,9.131949), (15,10.127788), (15.5,11.154043), (16,12.210073), (16.5,13.295218), (17,14.408806), (17.5,15.55016), (18,16.718603), (18.5,17.913469), (19,19.134105), (19.5,20.379886), (20,21.650216 The curve focusing surface is divided into 46 intervals with a step size h=0.5. (20.5,22.944546), (21,24.262373), (21.5,25.603254), (22,26.966812), (22.5,28.352743), (23,29.760819), (23.5,31.190896), (24,32.642909), (24.5,34.116879), (25,35.612902). In this embodiment, the iteration error d is 1.02 mm, and the maximum deviation e is... max The value is 1.68 mm, satisfying the iteration error d ≤ 2 mm and e max If the deviation is ≤2mm, and this level is within the allowable range of a precision optical system, then the geometric model is reliable; S4. The discrete point lattice of the surface geometric coordinates is fitted with a natural cubic spline curve, using natural boundary conditions, and setting the second derivative of the first and last endpoints to zero, i.e., M0=0 and M 46 =0, and the second derivatives M1 to M of each internal node are obtained by the chasing method. 45The values ​​are 0.290005, 0.458721, 0.447384, 0.354712, 0.316884, 0.285412, 0.258124, 0.234156, 0.212874, 0.193845, 0.176721, 0.153412, 0.132845, 0.114712, 0.097124, 0.086312, 0.076845, 0.068451, 0.061032, 0.054456, 0.048632, 0.043471, and 0.0388 respectively. 94, 0.034832, 0.031221, 0.029012, 0.027154, 0.025432, 0.023871, 0.022456, 0.021184, 0.019456, 0.017841, 0.016335, 0.014932, 0.013624, 0.012405, 0.011271, 0.010214, 0.009231, 0.008314, 0.007461, 0.006665, 0.005924, 0.003112, in each interval [x i x i+1 On the [x], a curved focusing surface is constructed using the formula in the interval [x] i x i+1 The surface equation of ] is used to generate a curved surface condenser model in 3D modeling software based on the surface equation of each interval; the interval [x] i x i+1 The equation formula for the surface shape of ] is: S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 ; In the formula, S i (x) is the surface shape function of the i-th interval, a i Let y be the ordinate of the left endpoint of the i-th interval. i b i The coefficient of the linear term in the polynomial represents the curve at x. i The slope at c i For M i / 2,d i The coefficients of the cubic term in the polynomial represent the interval [x]. i x i+1 The rate of change of the inner second derivative, b i The formula for calculation is: ; d i The formula for calculation is: ; In the formula, M i+1 For the interval [x i x i+1 Internal node x i+1 The second derivative, M i For the interval [x i x i+1 Internal node x i The second derivative, where h is the step size; The 46-segment piecewise fitting curve equations of the concentrator surface shape were calculated and obtained as follows: (1) In the interval [2.0, 2.5], S0(x)=-5.0+0.308771(x-2.0)+0.096668(x-2.0) 3 ; (2) In the interval [2.5, 3.0], S1(x)=-4.833531+0.381272(x-2.5)+0.145003(x-2.5) 2 +0.112477(x-2.5) 3 ; (3) In the interval [3.0, 3.5], S2(x)=-4.636522+0.465918(x-3.0)+0.229361(x-3.0) 2 -0.007558(x-3.0) 3 ; (4) In the interval [3.5, 4.0], S3(x)=-4.408408+0.569426(x-3.5)+0.218024(x-3.5) 2 -0.061781(x-3.5) 3 ; (5) In the interval [4.0, 4.5], S4(x)=-4.148634+0.640751(x-4.0)+0.125352(x-4.0) 2 -0.025219(x-4.0) 3 ; (6) In the interval [4.5, 5.0], S5(x)=-3.856666+0.697189(x-4.5)+0.087524(x-4.5) 2 -0.020982(x-4.5) 3 ; (7) In the interval [5.0, 5.5], S6(x)=-3.531995+0.741005(x-5.0)+0.056051(x-5.0) 2 -0.018192(x-5.0) 3 ; (8) In the interval [5.5, 6.0], S7(x)=-3.174151+0.772541(x-5.5)+0.028763(x-5.5) 2 -0.015977(x-5.5) 3 ; (9) In the interval [6.0, 6.5], S8(x)=-2.782713+0.793215(x-6.0)+0.004798(x-6.0) 2 -0.014187(x-6.0) 3 ; (10) In the interval [6.5, 7.0], S9(x)=-2.357307+0.804152(x-6.5)-0.016483(x-6.5) 2 -0.012693(x-6.5) 3 ; (11) In the interval [7.0, 7.5], S 10 (x)=-1.897622+0.825143(x-7.0)-0.035522(x-7.0) 2 -0.011429(x-7.0) 3 ; (12) In the interval [7.5, 8.0], S 11 (x)=-1.403408+0.852104(x-7.5)-0.052665(x-7.5) 2 -0.010341(x-7.5) 3 ; (13) In the interval [8.0, 8.5], S 12(x)=-0.874479+0.881452(x-8.0)-0.068177(x-8.0) 2 -0.009395(x-8.0) 3 ; (14) In the interval [8.5, 9.0], S 13 (x)=-0.310717+0.913101(x-8.5)-0.082269(x-8.5) 2 -0.008564(x-8.5) 3 ; (15) In the interval [9.0, 9.5], S 14 (x)=0.287930+0.946954(x-9.0)-0.095115(x-9.0) 2 -0.007828(x-9.0) 3 ; (16) In the interval [9.5, 10.0], S 15 (x)=0.921450+0.982912(x-9.5)-0.106857(x-9.5) 2 -0.007172(x-9.5) 3 ; (17) In the interval [10.0, 10.5], S 16 (x)=1.589767+1.020885(x-10.0)-0.117615(x-10.0) 2 -0.006584(x-10.0) 3 ; (18) In the interval [10.5, 11.0], S 17 (x)=2.292747+1.060784(x-10.5)-0.127491(x-10.5) 2 -0.006053(x-10.5) 3 ; (19) In the interval [11.0, 11.5], S 18 (x)=3.030197+1.102521(x-11.0)-0.136570(x-11.0) 2 -0.005572(x-11.0) 3 ; (20) In the interval [11.5, 12.0], S 19 (x)=3.801876+1.146012(x-11.5)-0.144928(x-11.5) 2 -0.005134(x-11.5) 3 ; (21) In the interval [12.0, 12.5], S 20 (x)=4.607494+1.191174(x-12.0)-0.152629(x-12.0) 2 -0.004735(x-12.0) 3 ; (22) In the interval [12.5, 13.0], S 21 (x)=5.446722+1.237931(x-12.5)-0.159732(x-12.5) 2 -0.004369(x-12.5) 3 ; (23) In the interval [13.0, 13.5], S 22 (x)=6.319192+1.286214(x-13.0)-0.166285(x-13.0) 2 -0.004033(x-13.0) 3 ; (24) In the interval [13.5, 14.0], S 23 (x)=7.224505+1.335952(x-13.5)-0.172335(x-13.5) 2 -0.003725(x-13.5) 3 ; (25) In the interval [14.0, 14.5], S 24 (x)=8.162239+1.387081(x-14.0)-0.177922(x-14.0) 2 -0.003441(x-14.0) 3 ; (26) In the interval [14.5, 15.0], S 25 (x)=9.131949+1.439542(x-14.5)-0.183084(x-14.5) 2 -0.003179(x-14.5)3 ; (27) In the interval [15.0, 15.5], S 26 (x)=10.127788+1.493284(x-15.0)-0.187852(x-15.0) 2 -0.002937(x-15.0) 3 ; (28) In the interval [15.5, 16.0], S 27 (x)=11.154043+1.548252(x-15.5)-0.192258(x-15.5) 2 -0.002713(x-15.5) 3 ; (29) In the interval [16.0, 16.5], S 28 (x)=12.210073+1.604401(x-16.0)-0.196328(x-16.0) 2 -0.002506(x-16.0) 3 ; (30) In the interval [16.5, 17.0], S 29 (x)=13.295218+1.661684(x-16.5)-0.200087(x-16.5) 2 -0.002313(x-16.5) 3 ; (31) In the interval [17.0, 17.5], S 30 (x)=14.408806+1.720054(x-17.0)-0.203556(x-17.0) 2 -0.002135(x-17.0) 3 ; (32) In the interval [17.5, 18.0], S 31 (x)=15.550160+1.779471(x-17.5)-0.206759(x-17.5) 2 -0.001969(x-17.5) 3 ; (33) In the interval [18.0, 18.5], S 32(x)=16.718603+1.839892(x-18.0)-0.209712(x-18.0) 2 -0.001815(x-18.0) 3 ; (34) In the interval [18.5, 19.0], S 33 (x)=17.913469+1.901284(x-18.5)-0.212435(x-18.5) 2 -0.001671(x-18.5) 3 ; (35) In the interval [19.0, 19.5], S 34 (x)=19.134105+1.963604(x-19.0)-0.214941(x-19.0) 2 -0.001537(x-19.0) 3 ; (36) In the interval [19.5, 20.0], S 35 (x)=20.379886+2.026824(x-19.5)-0.217247(x-19.5) 2 -0.001411(x-19.5) 3 ; (37) In the interval [20.0, 20.5], S 36 (x)=21.650216+2.090912(x-20.0)-0.219364(x-20.0) 2 -0.001293(x-20.0) 3 ; (38) In the interval [20.5, 21.0], S 37 (x)=22.944546+2.155841(x-20.5)-0.221303(x-20.5) 2 -0.001183(x-20.5) 3 ; (39) In the interval [21.0, 21.5], S 38 (x)=24.262373+2.221584(x-21.0)-0.223078(x-21.0) 2 -0.001079(x-21.0) 3 ; (40) In the interval [21.5, 22.0], S 39 (x)=25.603254+2.288112(x-21.5)-0.224696(x-21.5) 2 -0.000982(x-21.5) 3 ; (41) In the interval [22.0, 22.5], S 40 (x)=26.966812+2.355401(x-22.0)-0.226169(x-22.0) 2 -0.000891(x-22.0) 3 ; (42) In the interval [22.5, 23.0], S 41 (x)=28.352743+2.423424(x-22.5)-0.227506(x-22.5) 2 -0.000805(x-22.5) 3 ; (43) In the interval [23.0, 23.5], S 42 (x)=29.760819+2.492164(x-23.0)-0.228713(x-23.0) 2 -0.000724(x-23.0) 3 ; (44) In the interval [23.5, 24.0], S 43 (x)=31.190896+2.561592(x-23.5)-0.229799(x-23.5) 2 -0.000649(x-23.5) 3 ; (45) In the interval [24.0, 24.5], S 44 (x)=32.642909+2.631684(x-24.0)-0.230773(x-24.0) 2 -0.000578(x-24.0) 3 ; (46) In the interval [24.5, 25.0], S 45(x)=34.116879+2.702412(x-24.5)-0.231640(x-24.5) 2 -0.000511(x-24.5) 3 ; The first and second derivatives of the curved focusing surface are continuous at the connection points by using a cubic spline interpolation algorithm to eliminate false hot spots in optical simulation. S5. Using the ray tracing software Tracepro, the energy flux density distribution in different regions of the cylindrical absorber surface was simulated under the condition of perpendicular sunlight incidence (0° incident angle). The uniformity of the energy flux density distribution was verified by analyzing the energy flux density distribution map. Specifically, the curved surface concentrator model constructed according to the mathematical model was simulated in Tracepro under the condition of 0° incident angle to obtain the energy flux density distribution on the surface of the cylindrical absorber. The distribution of reflected light on the curved surface of the cylindrical absorber with radius r=2 was tracked and captured, and the total absorbed luminous flux of the system was found to be 880.4W, with the average energy flux density calculated to be 4.15kW / m². 2 The energy flux density is compared with the energy flux density at each point. If the deviation of the energy flux density of the entire light-receiving area from the average value does not exceed ±10%, the energy flux density distribution is considered to be uniform. Otherwise, the central angle β corresponding to the incident light rays incident on the cylindrical absorber is adjusted and redesigned until the condition for uniform energy flux density distribution is met. In this embodiment, the energy flux density of all light-receiving areas deviates from the average value by 6.7%, which is less than the preset threshold of 10%. Therefore, the energy flux density distribution on the cylindrical absorption surface in this embodiment is uniform.

[0018] The specific embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for constructing a curved solar concentrator with uniform light reception on the surface of the absorber, characterized in that, The curved solar concentrator includes a curved concentrating surface (1) and a cylindrical absorber (2). The cylindrical absorber (2) is disposed on the inner side of the curved surface of the curved concentrating surface (1). The curved concentrating surface (1) is used to uniformly reflect the sunlight that is perpendicularly incident on the curved concentrating surface (1) to the light-receiving surface of the cylindrical absorber (2), forming a uniform energy flux density distribution. The specific steps are as follows: S1. Obtain initial design parameters. Establish a Cartesian coordinate system with the center of the absorber as the origin O. The radius of the cylindrical absorber is r, the geometric concentration ratio of the curved solar concentrator is C, the central angle corresponding to the incident ray incident on the cylindrical absorber is β, and the incident parallel ray enters the concentrator opening along the negative y-axis. S2. Based on the initial design parameters, construct a mathematical model of the geometric relationship of the reflector surface of the curved solar concentrator and generate a three-dimensional curved surface. Establish a first-order nonlinear differential equation between the abscissa x and ordinate y of the reflector surface of the concentrator and the radius r of the cylindrical absorber. S3. When the central angle β corresponding to the incident light ray incident on the cylindrical absorber is greater than zero, β is iteratively calculated with a step size h. The convergence criterion is set as the iteration error d not exceeding 2mm and the maximum deviation e. max The iteration error d is no greater than 2mm, and the iteration error is the coordinate point (x) obtained from two adjacent iterations. i y i ), (x i+1 y i+1 The straight-line distance between them; Based on the current point coordinates and the derivative of the first-order nonlinear differential equation at that point, the next iteration point is predicted using the linear equation, and iterative calculation is performed until convergence. If the iteration error is greater than 2mm, the feedback optimization mechanism is activated, the central angle β is finely adjusted by ±1°, and iterative calculation is performed again until convergence, so as to obtain the discrete point lattice of surface geometric coordinates at each position of the curved light-collecting surface. S4. The discrete point lattice of the surface geometric coordinates is fitted with a spline curve, using natural boundary conditions, and the second derivatives of the first and last endpoints are set to zero, i.e., M0=0 and M n =0, and the second derivatives M1 to M of each internal node are obtained by the chasing method. n-1 In each interval [x i x i+1 On the [x], a curved focusing surface is constructed using the formula in the interval [x] i x i+1 The surface equation of ] is used to generate a curved surface condenser model in 3D modeling software based on the surface equation of each interval; S5. Using the ray tracing software Tracepro, simulate the energy flux density distribution in different regions of the cylindrical absorber surface under the condition of perpendicular sunlight incident at an incident angle of 0°. By analyzing the energy flux density distribution map, verify the uniformity of the energy flux density distribution.

2. The method for constructing a curved solar concentrator with uniform light reception on the surface of the absorber according to claim 1, characterized in that: The differential equations between the x-coordinate and y-coordinate of the concentrator reflector surface and the radius r of the cylindrical absorber in step S2 are as follows: ； The formula for calculating β is: ； In the formula, x is the abscissa of the curved solar concentrator, y is the ordinate of the curved solar concentrator, r is the radius of the cylindrical absorber, and β is the central angle corresponding to the incident light rays incident on the cylindrical absorber.

3. The method for constructing a curved solar concentrator with uniform light reception on the absorber surface according to claim 2, characterized in that: The formula for calculating the iteration error d in step S3 is as follows: ； The iterative calculation method for the central angle β corresponding to the incident light ray incident on the cylindrical absorber is as follows: β0 is 0, β n It is 0.5π. The , ； In the formula, β i For the i-th discrete point (x) i ,y i At point ), the central angle corresponding to the incident ray incident on the cylindrical absorber, β i-1 For the (i-1)th discrete point (x) i-1 ,y i-1 At point ( ), the central angle corresponding to the incident ray incident on the cylindrical absorber, r is the radius of the cylindrical absorber, h is the step size of the iterative calculation, and C con,i The geometric concentration ratio contributed by the reflective surface of the curved solar concentrator in the i-th iteration.

4. The method for constructing a curved solar concentrator with uniform light reception on the surface of the absorber according to claim 1, characterized in that: In step S4, the interval [x] i x i+1 The equation formula for the surface shape of ] is: S i (x)=a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 ; In the formula, S i (x) is the surface shape function of the i-th interval, a i Let y be the ordinate of the left endpoint of the i-th interval. i b i The coefficient of the linear term in the polynomial represents the curve at x. i The slope at c i For M i / 2,d i The coefficients of the cubic term in the polynomial represent the interval [x]. i x i+1 The rate of change of the inner second derivative, b i The formula for calculation is: ； d i The formula for calculation is: ； In the formula, M i+1 For the interval [x i x i+1 Internal node x i+1 The second derivative, M i For the interval [x i x i+1 Internal node x i The second derivative of , where h is the step size.

5. The method for constructing a curved solar concentrator with uniform light reception on the absorber surface according to claim 1, characterized in that: The method for verifying the uniformity of energy flux density distribution in step S5 is as follows: In step S5, the curved surface concentrator model constructed according to the mathematical model is simulated in Tracepro under the condition of 0° incident angle to obtain the energy flux density distribution on the surface of the cylindrical absorber; the average value of the energy flux density is calculated and compared with the energy flux density at each point; if the deviation of the energy flux density of the entire light-receiving area from the average value does not exceed ±10%, the energy flux density distribution is considered to be uniform; otherwise, the central angle β corresponding to the incident light rays incident on the cylindrical absorber is adjusted and redesigned until the condition for uniform energy flux density distribution is met.

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